1. Yale lectures 3 and 4 review Iterative deletion of dominated strategies. Ex: two players choose positions on political spectrum. Endpoints become repeatedly eliminated by deletion of dominated strategies.

2. Median Voter Theorem 12345678910 15,51,91.5,8.52,82.5,7.53,73.5,6.54,64.5,5.55,5 29,15,52,82.5,7.53,73.5,6.54,64.5,5.55,55.5,4.5 38.5,1.58,25,53,73.5,6.54,64.5,5.55,55.5,4.56,4 48,27.5,2.54,65,54,64.5,5.55,55.5,4.56,46.5,3.5 57.5,2.5 7,3 6.5,3.5 6,4 5,5 5.5,4.56,46.5,3.57,3 6 6,5,3.56,4 5.5,4.5 5,5 6,46.5,3.57,37.5,2.5 7 6.5,3.5 6,45.5,4.5 5,5 4.5,5.54,6 5,57,37.5,2.58,2 8 6,4 5.5,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 5,58,28.5,1.5 95.5,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,85,59,1 105,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,81.5,8.5 1,95,5

3. Median Voter Theorem 12345678910 15,51,91.5,8.52,82.5,7.53,73.5,6.54,64.5,5.55,5 29,15,52,82.5,7.53,73.5,6.54,64.5,5.55,55.5,4.5 38.5,1.58,25,53,73.5,6.54,64.5,5.55,55.5,4.56,4 48,27.5,2.54,65,54,64.5,5.55,55.5,4.56,46.5,3.5 57.5,2.5 7,3 6.5,3.5 6,4 5,5 5.5,4.56,46.5,3.57,3 6 6,5,3.56,4 5.5,4.5 5,5 6,46.5,3.57,37.5,2.5 7 6.5,3.5 6,45.5,4.5 5,5 4.5,5.54,6 5,57,37.5,2.58,2 8 6,4 5.5,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 5,58,28.5,1.5 95.5,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,85,59,1 105,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,81.5,8.5 1,95,5

4. Median Voter Theorem 12345678910 15,51,91.5,8.52,82.5,7.53,73.5,6.54,64.5,5.55,5 29,15,52,82.5,7.53,73.5,6.54,64.5,5.55,55.5,4.5 38.5,1.58,25,53,73.5,6.54,64.5,5.55,55.5,4.56,4 48,27.5,2.54,65,54,64.5,5.55,55.5,4.56,46.5,3.5 57.5,2.5 7,3 6.5,3.5 6,4 5,5 5.5,4.56,46.5,3.57,3 6 6,5,3.56,4 5.5,4.5 5,5 6,46.5,3.57,37.5,2.5 7 6.5,3.5 6,45.5,4.5 5,5 4.5,5.54,6 5,57,37.5,2.58,2 8 6,4 5.5,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 5,58,28.5,1.5 95.5,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,85,59,1 105,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,81.5,8.5 1,95,5

5. Median Voter Theorem 12345678910 15,51,91.5,8.52,82.5,7.53,73.5,6.54,64.5,5.55,5 29,15,52,82.5,7.53,73.5,6.54,64.5,5.55,55.5,4.5 38.5,1.58,25,53,73.5,6.54,64.5,5.55,55.5,4.56,4 48,27.5,2.54,65,54,64.5,5.55,55.5,4.56,46.5,3.5 57.5,2.5 7,3 6.5,3.5 6,4 5,5 5.5,4.56,46.5,3.57,3 6 6,5,3.56,4 5.5,4.5 5,5 6,46.5,3.57,37.5,2.5 7 6.5,3.5 6,45.5,4.5 5,5 4.5,5.54,6 5,57,37.5,2.58,2 8 6,4 5.5,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 5,58,28.5,1.5 95.5,4.5 5,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,85,59,1 105,54.5,5.5 4,6 3.5,6.5 3,7 2.5,7.5 2,81.5,8.5 1,95,5

6. Best Response No dominated strategies leftright U5,10,2 M1,34,1 R4,22,3

7. In this case… Each of player 1’s actions is a best response to some mixed strategy of player 2. If you have an action that is never a best response, don’t play it. The best response is the strategy (or strategies) which produces the most favorable outcome for a player, taking other players' strategies as given.

8. Finding a mutual best response Partnership game b is synergy. s 1 and s 2 are effort levels. Max s1 2(s 1 + s 2 +bs 1 s 2 ) –(s 1 ) 2 Use calculus – differentiate and set to zero 2(1+bs 2 ) –2(s 1 ) = 0 1+bs 2 =(s 1 ) Best response function for s 1 1+bs 1 =(s 2 ) Best response function for s 2 if equal (as symmetric), 1+b(1+bs 1 ) =(s 1 ) s 1 = 1/(1-b) Your share of the profit Your cost of effort

9. Mutual Best response graph if b=1/4

10. Nash Equilibrium If we are at a Nash Equilibrium, neither player has an incentive to deviate.